Dataviz principles

17-3-7

Introduction

These slides are inspired by:

"Creating effective figures and tables" by Karl Broman. Code available on GitHub repository. Introduction to Data Visualization course by Peter Aldhous

It is a chapter in a data visualization chapter in this book

Introduction

We show some examples of plot styles we should avoid, explain how to improve them, and use these as motivation for a list of principles.
We compare and contrast plots that follow these principles to those that don't.

Introduction

The principles are mostly based on research related to how humans detect patterns and make visual comparisons.
The preferred approaches are those that best fit the way our brains process visual information.
When deciding on a visualization approach it is also important to keep our goal in mind.
We may be comparing a viewable number of quantities, describing distribution for categories or numeric values, comparing the data from two groups, or describing the relationship between two variables.

Encoding data using visual cues

We start by describing some principles for encoding data.
There are several approaches at our disposal including:
- position
- aligned lengths
- angles
- area
- brightness
- color hue.

First example

To illustrate how some of these strategies compare let's suppose we want to report the results from two hypothetical polls asking regarding browser preference taken in 2000 and then 2015.
Here, for each year, we are simply comparing four quantities, four percentages.
A widely used graphical representation of percentages, popularized by Microsoft Excel, is the pie chart:

First example

Encoding data with angles and areas: not recommended

Here we are representing quantities with both areas and angles since both the angle and area of each pie slice is proportional to the quantity it represents.
This turns out to be a sub optimal choice since, as demonstrated by perception studies, humans are not good at precisely quantifying angles and are even worse when only are is available.

Encoding data with just area: even less recommended

Pie chart of browser usage.

Pie charts

To see how hard it is to quantify angles and are note that the rankings and all the percentages in the plots above changed fro 2000 to 2015.
Can you determine the actual percentages and rank the browsers' popularity? Can you see how the percentages changed from 2000 to 2015? It is not easy to tell from the plot.

Pie charts

In this case, simply showing the numbers is not only clearer, but it would saves on print cost if making a paper version.

Browser	2000	2015
Opera	3	2
Safari	21	22
Firefox	23	21
Chrome	26	29
IE	28	27

barplots

The preferred way to plot quantities is to use length and position since humans are much better at judging linear measure.
The barplot uses bars use this approach by using bars of length proportional to the quantities of interest.
By adding horizontal lines at strategically chosen values, in this case at every multiple of 10, we ease the quantifying through the position of the top of the bars.

pie chart vs barplots

If forced to make a pie chart at percentages

Visual cues

Position and length are the preferred ways to display quantities over angles which are preferred to area.
Brightness and color are even harder to quantifying that angles and area but, as we will see later, they are sometimes useful when more than two dimensions are being displayed.

When to include 0

When using length (e.g. barplots) it is misleading not to start the bars at 0.
This is because, by using a barplot, we are implying the length is proportional to the quantities being displayed.
By avoiding 0, relatively small difference can be made to look much bigger than they actually are.
This approach is often used by politicians or media organizations trying to exaggerate a difference.

Example

(Source: Fox News, via Media Matters via Fox News via Peter Aldhous

Same data with plot that includes 0

Another example

Via Fox News via Flowingdata

Same data with plot the includes 0

When not to include 0

When using position rather than length, it is not necessary to include 0.
This is particularly the case when we want to compare differences between groups relative the variability seen within the groups.

Example: Life expectancy by continent in 2012

Do not distrort quantities

(Source: President Barack Obama’s 2011 State of the Union Address via [Peter Aldhous] (http://paldhous.github.io/ucb/2016/dataviz/index.html))

Do not distrort quantities

The reason for this distortion is that the radius, rather than the area, was made to be proportional to the quantity.
This implies that the proportion between the areas is squared: 2.6 turns into 6.5 and 5.8 turns into 34.1.

Use area not radius

But we should not be using area or radius

Order by a meaningful value

When one of the axes is used to show categories, as is done in barplots, the default ggplot behavior is to order the categories alphabetically when they are defined by character strings.
If they are defined by factors, they are ordered by the factor levels.
We rarely want to use alphabetical order.
Instead we should order by a meaningful quantity.

Order by a meaningful value

Another example: Average income by region in 1970 (colors = continent)

Show the data

To motivate this principle let's asssume an extraterrestrial is interested is the difference in heights between males and females.
A commonly seen plot used for comparisons between groups, popularized by software such as Microsoft Excel, shows the average and standard errors (standard errors are defined in a later chapter, but don't confuse them with the standard deviation of the data).

Show the data

What do we learn? We get an idea of the range of the data.
However this plot has limitations as well since we can't really see all the 238 and 812 points plotted for females and males respectively, and many points are plotted above each other.

jitter and alpha blending

Show the data

What do we learn? On average, males are taller than females.
We also note dark horizontal demonstrating that many report values are rounded to the nearest integer.
Since there are so many points it is more effective to show distributions, rather than show individual points.

Compare distributions if too many points

Ease comparisons: Use common axes

Ease comparisons: align vertically

Ease comparisons

This plot makes it much easier to notice that men are, on average, taller.
If instead of histograms we want the more compact summary provided by boxplot, then we align the horizontally, since, by default, boxplots move up and down with changes in height.

Ease comparisons: align horizontally

Comparison

grid.arrange(p1, p2, p3, ncol = 3)

Consider transformations

As an example consider this barplot showing the average population sizes for each continent in 2015:

Consider transformations

Show the data

Consider transformations

Ease comparisons

Visual cues to be compared should be adjacent
When comparing income data between 1970 and 2010 across region we made a figure similar to the one below.
A difference is that here we look at continents instead of regions, but this is not relevant to the point we are making.

Ease comparisons

Comparisons should be adjacent

Use color to highlight comparison

Think of the color blind

Use scatter-plots to examine the relationship between two variables

Exceptions are

Slope charts
Bland-Altman plots

Slope charts

Scatter plot (with common axes)

Bland-Altman plot

Encoding a third variable

Note that we encode categorical variables with color hue and shape.
These shape can be controlled with shape argument.
Below are the shapes available for use in R.
Note that for the last five, the color goes inside.

Encoding a third variable

For continuous variables we can use color, intensity or size.
We now show an example of how we do this with a case study.

Example

The data used for these plots were collected, organized and distributed by the Tycho Project.
They include weekly reported counts data for seven diseases from 1928 to 2011, from all fifty states.

One state is easy

We need other cues for third dimenion

When choosing colors to quantify a numeric variable we chose between two options sequential and diverging.
Sequential colors are suited for data that goes from high to low.
High values are clearly distinguished from low values.
Here are some examples offered by the package RColorBrewer

Paletts

Diverging colors are used to represent values that diverge from a center.
We put equal emphasis on both ends of the data range: higher than the center and lower than the center.
An example of when we would use a divergent pattern would be if we were to show height in standard deviations away from the average.
Here are some examples of divergent patterns:

Sequential Paletts

Divergent Paletts

library(RColorBrewer)
display.brewer.all(type="div")

Example

Alternative: eliminate one variable

Avoid pseudo three dimensional plots

(Source: Karl Broman)

Avoid pseudo three dimensional plots

Avoid gratuitousthree dimensional plots

Pseudo 3D is sometimes used completely gratuitously: plots are made to look 3D even when the 3rd dimension does not represent a quantity.
This only adds confusion and makes it harder to relay your message.

Avoid gratuitousthree dimensional plots

Avoid too any significant digits

By default, statistical software like R returns many significant digits.
The default behavior in R is to show 7 significant digits.
So many digits often adds no information and the visual clutter than can makes it hard for the consumer of your table to understand the message.
As an example here are the per 10,000 disease rates for California across the five decades

Avoid too any significant digits

state	year	Measles	Pertussis	Polio
California	1940	37.8826320	18.3397861	18.3397861
California	1950	13.9124205	4.7467350	4.7467350
California	1960	14.1386471	0.0000000	0.0000000
California	1970	0.9767889	0.0000000	0.0000000
California	1980	0.3743467	0.0515466	0.0515466

Avoid too any significant digits

We are reporting precision up to 0.00001 cases per 10,000, a very small value in the context the changes that are occurring across the dates.
In this case 2 significant figure is more than enough and makes the point that rates are decreasing clearly:

Avoid too any significant digits

## `mutate_each()` is deprecated.
## Use `mutate_all()`, `mutate_at()` or `mutate_if()` instead.
## To map `funs` over a selection of variables, use `mutate_at()`

state	year	Measles	Pertussis	Polio
California	1940	37.9	18.3	18.3
California	1950	13.9	4.7	4.7
California	1960	14.1	0.0	0.0
California	1970	1.0	0.0	0.0
California	1980	0.4	0.1	0.1

Compare vertically

Another principle, related to displaying tables, is to place values being compared on columns rather than rows.

Compare vertically

## `mutate_each()` is deprecated.
## Use `mutate_all()`, `mutate_at()` or `mutate_if()` instead.
## To map `funs` over a selection of variables, use `mutate_at()`

state	year	Measles	Pertussis	Polio
California	1940	37.9	18.3	18.3
California	1950	13.9	4.7	4.7
California	1960	14.1	0.0	0.0
California	1970	1.0	0.0	0.0
California	1980	0.4	0.1	0.1

Do not compare horizontally

## `mutate_each()` is deprecated.
## Use `mutate_all()`, `mutate_at()` or `mutate_if()` instead.
## To map `funs` over a selection of variables, use `mutate_at()`

state	disease	1940	1950	1960	1970	1980
California	Measles	37.9	13.9	14.1	1	0.4
California	Pertussis	18.3	4.7	0.0	0	0.1
California	Polio	18.3	4.7	0.0	0	0.1